Submissions are evaluated on the **Area Under the ROC Curve (AUC-ROC)** between the predicted probability and the observed target. This metric is well-suited for binary classification problems with class imbalance, as it measures the ability of the model to distinguish between the two classes (implant survival vs. failure) across all possible thresholds.

### Submission File Format

For each `patient_id` in the test set, you must predict a probability for the `implant_survival_10_years` target variable. The file should contain a header and have the following format:

```
patient_id,implant_survival_10_years
1,0.95
2,0.12
3,0.88
etc.
```

The `implant_survival_10_years` column should contain the predicted probability of survival (a value between 0 and 1).